Class 8 Maths

# Factorisation

## Exercise 14.1

Question 1: Find the common factors of the given terms.

(i) 12x, 36

Answer: 12x=2xx2xx3xx\x

36=2xx2xx3xx3

Here, common factor = 2xx3=6

(ii) 2y, 22xy

Answer: 2y=2xx\y

22y=2xx11xx\y

Common factor = 2

(iii) 14 pq, 28 p2q2

Answer: 14pq=2xx7xx\p\xx\q

28p^2q^2=2xx2xx7xx\p\xx\p\xx\q\xx\q

Common factor =2xx7xx\p\xx\q

(iv) 2x, 3x², 4

Answer: 2x=2xx\x

3x^2=3xx\x\xx\x

4=2xx2

Common factor = 1

There is no common factor other than unity, so common factor= 1

(v) 6 abc, 24ab², 12 a²b

Answer: 6abc=2xx3xx\a\xx\b\xx\c

24ab^2=2xx2xx2xx3xx\a\xx\b\xx\b

12a^2b=2xx2xx3xx\a\xx\a\xx\b

Common Factor =2xx3xx\a\xx\b

(vi) 16 x³, – 4x², 32x

Answer: 16x^3=2xx2xx2xx2xx\a\xx\a\xx\a

-4x^2=-2xx2xx\x\xx\x

32x=2xx2xx2xx2xx2xx\x

Common factor =2x

(vii) 10 pq, 20qr, 30rp

Answer: 10pq=2xx5xx\p\xx\q

20qr=2xx2xx4xx\q\xx\r

30rp=2xx3xx5xx\r\xx\p

Common factor =2xx5=10

(viii) 3x² y³, 10x³ y²,6 x² y²z

Answer: 3x^2y^3=3xx\x\xx\x\xx\y\xx\y\xx\y

10x^3y^2=2xx5xx\x\xx\x\xx\x\xx\y\xx\y

x^2y^2z=x\xx\x\xx\y\xxy\xx\z

Common factor=x^2y^2

Question 2: Factorise the following expressions.

(i) 7x – 42

Answer: 7x-42

=7xx\x-7xx6=7(x-6)

(ii) 6p – 12q

Answer: 6p-12q

=6xx\p-6xx2q=6(p-2q)

(iii) 7a² + 14a

Answer: 7a^2+14a

=7xx\a\xx\a+7xx2xx\a=7a(a+2)

(iv) – 16 z + 20 z³

Answer: -16z+20z^3

=4xx4xx\z+4xx5xx\z\xx\z\xx\z

=4z(-4+5z\xx\z)=4z(5z^2-4)

(v) 20 l² m + 30 a l m

Answer: 20l^2m+30alm

=2xx2xx5xx\l\xx\l\xx\m+2xx3xx5xx\a\xx\l\xx\m

=2lm(10l+15a)

(vi) 5 x² y – 15 xy²

Answer: 5x^2y-15xy^2

=5xx\x\xx\x\xx\y-3xx5xx\x\xx\y\xx\y

=5x(xy-3y^2)

(vii) 10 a² – 15 b² + 20 c²

Answer: 10a^2-15b^2+20c^2

=2xx5xx\a\xx\a-3xx5xx\b\xx\b+4xx5xx\c\xx\c

=5(2a^2-3b^2+4c^2)

(viii) – 4 a² + 4 ab – 4 ca

Answer: -4a^2+4ab-4ca

=-4xx\a\xx\a+4xx\a\xx\b-4xx\c\xx\a

=-4a(a-b+c)

(ix) x² y z + x y²z + x y z²

Answer: x^2yz+xy^2z+xyz^2

=x\xx\x\xx\y\xx\z+x\xx\y\xx\y\xx\z+x\xx\y\xx\z\xx\z

=xyz(x+y+z)

(x) a x² y + b x y² + c x y z²

Answer: ax^yz+bxy^2z+cxyz^2

=a\xx\x\xx\x\xx\y\xx\z+b\xx\x\xx\y\xx\y\xx\z+c\xx\x\xx\y\xx\z\xx\z

=xyz(ax+by+cz)

Question 3: Factorise.

(i) x² + x y + 8x + 8y

Answer: x^2+xy+8x+8y

=x\xx\x+x\xx\y+8xx\x+8xx\y

=x(x+y)+8(x+y)

=(x+8)(x+y)

(ii) 15 xy – 6x + 5y – 2

Answer: 15xy-6x+5y-2

=3xx5xx\x\xx\y-2xx3xx\x+5xx\y-2

=3x(5y-2)+1(5y-2)

=(3x+1)(5y-2)

(iii) ax + bx – ay – by

Answer: ax+bx-ay-by

=x(a+b)-y(a+b)

=(x-y)(a+b)

(iv) 15 pq + 15 + 9q + 25p

Answer: 15pq+15+9q+25p

=5xx3xx\pq+5xx3+3xx3q+5xx5p

=5xx3pq+3xx3q+5xx5p+5xx3

=3q(5p+3)+5(5p+3)

=(3q+5)(5p+3)

(v) z – 7 + 7 x y – x y z

Answer: z-7+7xy-xyz

=z-xyz-7+7xy

=z(1-xy)-7(1-xy)

=(z-7)(1-xy)